6x^2-5000=0

Solution for 6x^2-5000=0 equation:

6x^2-5000=0

a = 6; b = 0; c = -5000;
Δ = b2-4ac
Δ = 02-4·6·(-5000)
Δ = 120000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120000}=\sqrt{40000*3}=\sqrt{40000}*\sqrt{3}=200\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{3}}{2*6}=\frac{0-200\sqrt{3}}{12}
=-\frac{200\sqrt{3}}{12}
=-\frac{50\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{3}}{2*6}=\frac{0+200\sqrt{3}}{12}
=\frac{200\sqrt{3}}{12}
=\frac{50\sqrt{3}}{3}
$